$G_2$-Holonomy Metrics Connected with a 3-Sasakian Manifold

TL;DR

This paper constructs new complete noncompact metrics with $G_2$-holonomy on orbifolds structured as $R^3$-bundles over twistor spaces, expanding the known examples in special holonomy geometry.

Contribution

It introduces explicit constructions of $G_2$-holonomy metrics on orbifolds with $R^3$-bundle structures over twistor spaces, linking special holonomy with complex geometric structures.

Findings

Explicit $G_2$-holonomy metrics on orbifolds

Connection between $G_2$-holonomy and twistor geometry

Complete noncompact examples with orbifold singularities

Abstract

We construct complete noncompact Riemannian metrics with $G_2$-holonomy on noncompact orbifolds that are $\Bbb R^3$-bundles with the twistor space $\mathcal{Z}$ as a spherical fiber.